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At least 487 records · Page 27

Students as Ground Observers for Satellite Cloud Retrieval Validation

The Students' Cloud Observations On-Line (S'COOL) Project was initiated in 1997 to obtain student observations of clouds coinciding with the overpass of the Clouds and the Earth's Radiant Energy System (CERES) instruments on NASA's Earth Observing System satellites. Over the past seven years we have accumulated more than 9,000 cases worldwide where student observations are available within 15 minutes of a CERES observation. This paper reports on comparisons between the student and satellite data as one facet of the validation of the CERES cloud retrievals. Available comparisons include cloud cover, cloud height, cloud layering, and cloud visual opacity. The large volume of comparisons allows some assessment of the impact of surface cover, such as snow and ice, reported by the students. The S'COOL observation database, accessible via the Internet at http://scool.larc.nasa.gov, contains over 32,000 student observations and is growing by over 700 observations each month. Some of these observations may be useful for assessment of other satellite cloud products. In particular, some observing sites have been making hourly observations of clouds during the school day to learn about the diurnal cycle of cloudiness.

Chambers, Lin H.↗

A Comparison of Aerosol Optical Property Measurements Made During the DOE Aerosol Intensive Operating Period and Their Effects on Regional Climate

The amount of radiant energy an aerosol absorbs has profound effects on climate and air quality. It is ironic that aerosol absorption coefficient is one of the most difficult to measure aerosol properties. One of the main purposes of the DOE Aerosol Intensive Operating Period (IOP) flown in May, 2003 was to assess our ability to measure absorption coefficient in situ. This paper compares measurements of aerosol optical properties made during the IOP. Measurements of aerosol absorption coefficient were made by Particle Soot Absorption Photometer (PSAP) aboard the CIRPAS Twin-Otter (U. Washington) and on the DOE Cessna 172 (NOAA-C,MDL). Aerosol absorption coefficient was also measured by a photoacoustic instrument (DRI) that was operated on an aircraft for the first time during the IOP. A new cavity ring-down (CRD) instrument, called Cadenza (NASA-AkC), measures the aerosol extinction coefficient for 675 nm and 1550 nm light, and simultaneously measures the scattering coefficient at 675 nm. Absorption coefficient is obtained from the difference of measured extinction and scattering within the instrument. Measurements of absorption coefficient from all of these instruments during appropriate periods are compared. During the IOP, several significant aerosol layers were sampled aloft. These layers are identified in the remote (AATS-14) as well as in situ measurements. Extinction profiles measured by Cadenza are compared to those derived from the Ames Airborne Tracking Sunphotometer (AATS-14, NASA-ARC). The regional radiative impact of these layers is assessed by using the measured aerosol optical properties in a radiative transfer model.

Strawa, Anthony W.↗

In-Situ Measurements of Aerosol Optical Properties using New Cavity Ring-Down and Photoacoustics Instruments and Comparison with more Traditional Techniques

Carbonaceous species (BC and OC) are responsible for most of the absorption associated with aerosol particles. The amount of radiant energy an aerosol absorbs has profound effects on climate and air quality. It is ironic that aerosol absorption coefficient is one of the most difficult aerosol properties to measure. A new cavity ring-down (CRD) instrument, called Cadenza (NASA-ARC), measures the aerosol extinction coefficient for 675 nm and 1550 nm light, and simultaneously measures the scattering coefficient at 675 nm. Absorption coefficient is obtained from the difference of measured extinction and scattering within the instrument. Aerosol absorption coefficient is also measured by a photoacoustic (PA) instrument (DRI) that was operated on an aircraft for the first time during the DOE Aerosol Intensive Operating Period (IOP). This paper will report on measurements made with this new instrument and other in-situ instruments during two field recent field studies. The first field study was an airborne cam;oaign, the DOE Aerosol Intensive Operating Period flown in May, 2003 over northern Oklahoma. One of the main purposes of the IOP was to assess our ability to measure extinction and absorption coefficient in situ. This paper compares measurements of these aerosol optical properties made by the CRD, PA, nephelometer, and Particle Soot Absorption Photometer (PSAP) aboard the CIRPAS Twin-Otter. During the IOP, several significant aerosol layers were sampled aloft. These layers are identified in the remote (AATS-14) as well as in situ measurements. Extinction profiles measured by Cadenza are compared to those derived from the Ames Airborne Tracking Sunphotometer (AATS-14, NASA-ARC). The regional radiative impact of these layers is assessed by using the measured aerosol optical properties in a radiative transfer model. The second study was conducted in the Caldecott Tunnel, a heavily-used tunnel located north of San Francisco, Ca. The aerosol sampled in this study was characterized by fresh automobile and diesel exhaust. Measurements from Cadenza and from an aethalometer are presented. The aethalometer is a filter-based photometer and the infrared channel is calibrated to produce a measure of BC mass loading.

Strawa, A. W.↗

Defining Top-of-Atmosphere Flux Reference Level for Earth Radiation Budget Studies

To estimate the earth's radiation budget at the top of the atmosphere (TOA) from satellite-measured radiances, it is necessary to account for the finite geometry of the earth and recognize that the earth is a solid body surrounded by a translucent atmosphere of finite thickness that attenuates solar radiation differently at different heights. As a result, in order to account for all of the reflected solar and emitted thermal radiation from the planet by direct integration of satellite-measured radiances, the measurement viewing geometry must be defined at a reference level well above the earth s surface (e.g., 100 km). This ensures that all radiation contributions, including radiation escaping the planet along slant paths above the earth s tangent point, are accounted for. By using a field-of- view (FOV) reference level that is too low (such as the surface reference level), TOA fluxes for most scene types are systematically underestimated by 1-2 W/sq m. In addition, since TOA flux represents a flow of radiant energy per unit area, and varies with distance from the earth according to the inverse-square law, a reference level is also needed to define satellite-based TOA fluxes. From theoretical radiative transfer calculations using a model that accounts for spherical geometry, the optimal reference level for defining TOA fluxes in radiation budget studies for the earth is estimated to be approximately 20 km. At this reference level, there is no need to explicitly account for horizontal transmission of solar radiation through the atmosphere in the earth radiation budget calculation. In this context, therefore, the 20-km reference level corresponds to the effective radiative top of atmosphere for the planet. Although the optimal flux reference level depends slightly on scene type due to differences in effective transmission of solar radiation with cloud height, the difference in flux caused by neglecting the scene-type dependence is less than 0.1%. If an inappropriate TOA flux reference level is used to define satellite TOA fluxes, and horizontal transmission of solar radiation through the planet is not accounted for in the radiation budget equation, systematic errors in net flux of up to 8 W/sq m can result. Since climate models generally use a plane-parallel model approximation to estimate TOA fluxes and the earth radiation budget, they implicitly assume zero horizontal transmission of solar radiation in the radiation budget equation, and do not need to specify a flux reference level. By defining satellite-based TOA flux estimates at a 20-km flux reference level, comparisons with plane-parallel climate model calculations are simplified since there is no need to explicitly correct plane-parallel climate model fluxes for horizontal transmission of solar radiation through a finite earth.

Loeb, N. G.↗

The CERES S'COOL Project: Operational but not Routine

The first Clouds and the Earth's Radiant Energy System (CERES) instrument has been returning useful data on Earth's radiation budget from the Tropical Rainfall Measuring Mission (TRMM) spacecraft since late 1997. Validation of the initial data is now intensively underway. As one component of this validation, the CERES Students Cloud Observations On-Line (S'COOL) project has been operational since April 1998 - the 2nd CERES validation month. S'COOL involves school children in over 140 schools in 15 countries on 5 continents in making and reporting observations and measurements which they and CERES scientists can then compare to the satellite retrievals. The project is planned to continue through the life of the CERES Project (nominally 15 years), and new participants are invited to join on a continuous basis. This paper will report on the first year of the operational phase of the project, during which a number of exciting events occurred (a demonstration of the project to First Lady Hillary Rodham Clinton, and visits by CERES personnel to participating schools, among others). It will further report on some of the noteworthy observations and comparisons which have been made possible by this project. We have found that schools are often located in interesting places, in terms of the clouds found there and the satellite's ability to observe these clouds. The paper will also report on the learning opportunities delivered by this project, and on new questions about the planet and its climate which arise in the students minds as a result of their active participation.

Chambers, Lin H.↗

Differences between ERBE and CERES Tropical Mean Fluxes: ENSO, Climate Change or Calibration?

Verner E. Soumi was the father of radiation budget measurements from space. He directed the team at the University of Wisconsin that developed the first radiation budget measurements on the Iota (Explorer VII) coverage) spacecraft in 1959. The first data published was from hand calculations of night-time long-wave fluxes, with absolute accuracy estimated as better than 10 percent, and the data shown as hand drawn maps with lines of equal "long-wave radiation loss, in Langleys per minute X 10(exp -3) (isolangleys)". The first comparisons of the new radiation data with nephanalyses showed that clouds dominated the radiation patterns. Soumi immediately proposed using the radiation fields to help understand the atmospheric heat sources necessary to drive the atmospheric circulation. This early work already pointed to the relationship between the outgoing longwave radiation at the top of the atmosphere and the vertical flux divergence of infrared radiation within the atmosphere. In the next 30 years, global satellite observations of the radiation balance of the planet have advanced both in accuracy, stability, and in their ability to address cause and effect in the climate system. The purpose of the present paper is to examine early results of the new Clouds and the Earth's Radiant Energy System (CERES) data on Tropical Rainfall Measuring System (TRMM) which started data collection in January, 1998. CERES is a direct descendant of the legacy of Soumi's foresight on understanding the global energetics using satellite observations of broadband radiation.

Wielicki, Bruce A.↗

Cloud Detection from Satellite Imagery: A Comparison of Expert-Generated and Automatically-Generated Decision Trees

Automated cloud detection and tracking is an important step in assessing global climate change via remote sensing. Cloud masks, which indicate whether individual pixels depict clouds, are included in many of the data products that are based on data acquired on- board earth satellites. Many cloud-mask algorithms have the form of decision trees, which employ sequential tests that scientists designed based on empirical astrophysics studies and astrophysics simulations. Limitations of existing cloud masks restrict our ability to accurately track changes in cloud patterns over time. In this study we explored the potential benefits of automatically-learned decision trees for detecting clouds from images acquired using the Advanced Very High Resolution Radiometer (AVHRR) instrument on board the NOAA-14 weather satellite of the National Oceanic and Atmospheric Administration. We constructed three decision trees for a sample of 8km-daily AVHRR data from 2000 using a decision-tree learning procedure provided within MATLAB(R), and compared the accuracy of the decision trees to the accuracy of the cloud mask. We used ground observations collected by the National Aeronautics and Space Administration Clouds and the Earth s Radiant Energy Systems S COOL project as the gold standard. For the sample data, the accuracy of automatically learned decision trees was greater than the accuracy of the cloud masks included in the AVHRR data product.

Shiffman, Smadar↗

Light-emitting diodes as an illumination source for plants: a review of research at Kennedy Space Center

The provision of sufficient light is a fundamental requirement to support long-term plant growth in space. Several types of electric lamps have been tested to provide radiant energy for plants in this regard, including fluorescent, high-pressure sodium, and metal halide lamps. These lamps vary in terms of spectral quality, which can result in differences in plant growth and morphology. Current lighting research for space-based plant culture is focused on innovative lighting technologies that demonstrate high electrical efficiency and reduced mass and volume. Among the lighting technologies considered for space are light-emitting diodes (LEDs). The combination of red and blue LEDs has proven to be an effective lighting source for several crops, yet the appearance of plants under red and blue lighting is purplish gray, making visual assessment of plant health difficult. Additional green light would make the plant leaves appear green and normal, similar to a natural setting under white light, and may also offer psychological benefits for the crew. The addition of 24% green light (500-600 nm) to red and blue LEDs enhanced the growth of lettuce plants compared with plants grown under cool white fluorescent lamps. Coincidentally, these plants grown under additional green light would have the additional aesthetic appeal of a green appearance.

NASA Discipline Life Support Systems↗

Solar Selective Coatings Developed for Space Power Applications

A solar collector having the combined properties of high solar absorptance, low infrared emittance, and high thermal conductivity is envisioned for space power applications on minisatellites. A high solar absorptance is needed to collect as much of the incident solar radiation as possible and a low infrared emittance is needed to minimize radiant energy losses. A lightweight material having a high thermal conductivity is needed to transport the absorbed energy to where it is needed. Such a solar collector may be used with a low temperature-differential heat engine to provide electric power to the minisatellite components or as a source of thermal energy for a thermal bus that would heat remote regions of the spacecraft. The key to such a collector is the use of cermet coatings. Cermet coatings are composed of molecular islands of metal embedded in a three-dimensional matrix of dielectric. Recent research on molecular mixtures of aluminum and aluminum oxide at the NASA Glenn Research Center has yielded cermet coatings with a solar absorptance a of 0.797 and an infrared emittance epsilon of 0.131, yielding an alpha/epsilon ratio of 6. Although additional work is needed to further increase the alpha/epsilon ratio, these coatings are attractive owing to their potential durability in the space environment. The aluminum oxide surface should provide substantial protection from the atomic oxygen found in low Earth orbit. To help minimize emittance, these coatings are deposited on a smooth surface. The selected surface is aluminum that has been diamond turned to a mirror finish. Cermet coatings are manufactured by sputter deposition. To achieve the desired variable composition, Glenn's researchers implemented a novel approach using a cylindrical target composed of aluminum and aluminum oxide. Rotating the cylinder during the deposition process yields a coating of variable composition. A photograph of the custom-made aluminum and aluminum oxide cylindrical target installed in the sputter deposition chamber is shown.

Jaworske, Donald A.↗

Comparison of Cloud Resolving Model Simulations to Remote Sensing Data

The purpose of this research was to evaluate the ability of a cloud-resolving model (CRM) to simulate the dynamical, radiative, and microphysical properties of deep convective cloud objects identified using CERES (Clouds and the Earth s Radiant Energy System) on board the Tropical Rainfall Measuring Mission (TRMM) satellite platform, for many cases. A deep convective cloud object is a contiguous region that is composed of satellite footprints that fulfill the following selection criteria: 100% cloud fraction, cloud optical depth > 10, and a cloud top height of at least 10 km. Selection criteria have also been formed for different types of boundary-layer clouds, as described in Xu et al. (2005). The purpose of the cloud object approach is to identify specific areas of where the cloud properties simulated by the CRM systematically differ from the observed cloud properties. Where these systematic differences exist, concrete steps can be made to improve the CRM s simulation of an entire class of clouds, rather than by tuning the model to correctly simulate a single case study, as is often done. Additional information regarding detailed approaches and findings are presented.

Randall, David A.↗

Detection and Retrieval of Multi-Layered Cloud Properties Using Satellite Data

Four techniques for detecting multilayered clouds and retrieving the cloud properties using satellite data are explored to help address the need for better quantification of cloud vertical structure. A new technique was developed using multispectral imager data with secondary imager products (infrared brightness temperature differences, BTD). The other methods examined here use atmospheric sounding data (CO2-slicing, CO2), BTD, or microwave data. The CO2 and BTD methods are limited to optically thin cirrus over low clouds, while the MWR methods are limited to ocean areas only. This paper explores the use of the BTD and CO2 methods as applied to Moderate Resolution Imaging Spectroradiometer (MODIS) and Advanced Microwave Scanning Radiometer EOS (AMSR-E) data taken from the Aqua satellite over ocean surfaces. Cloud properties derived from MODIS data for the Clouds and the Earth's Radiant Energy System (CERES) Project are used to classify cloud phase and optical properties. The preliminary results focus on a MODIS image taken off the Uruguayan coast. The combined MW visible infrared (MVI) method is assumed to be the reference for detecting multilayered ice-over-water clouds. The BTD and CO2 techniques accurately match the MVI classifications in only 51 and 41% of the cases, respectively. Much additional study is need to determine the uncertainties in the MVI method and to analyze many more overlapped cloud scenes.

Minnis, Patrick↗

Fast Longwave and Shortwave Radiative Flux (FLASHFlux) Products from CERES and MODIS Measurements

The Clouds and the Earth s Radiant Energy Systems (CERES) project is currently producing world-class climatological data products derived from measurements taken aboard the Terra and Aqua spacecrafts (Wielicki et al., 1996). While of exceptional fidelity, these data products require a considerable amount of processing to assure quality and verify accuracy and precision. Obtaining such high quality assurance, however, means that the CERES data is typically released more than six months after the acquisition of the initial measurements. For climate studies, such delays are of little consequence, especially considering the improved quality of the released data products. There are, however, many uses for the CERES data products on a near real-time basis. These include: CERES instrument calibration and subsystem quality checks, CLOUDSAT operations, seasonal predictions, agricultural and ocean assimilations, support of field campaigns, and outreach programs such as S'Cool. The FLASHflux project was envisioned as a conduit whereby CERES data could be provided to the community within a week of the initial measurements, with the trade-off that some degree of fidelity would be exacted to gain speed. In this paper, we will report on some very encouraging initial results from the FLASHflux project in which we compared the FLASHflux instantaneous surface fluxes to the CERES surface-only flux algorithm data products.

Stackhouse, Paul W., Jr.↗

Derivation of Improved Surface and TOA Broadband Fluxes Using CERES-derived Narrowband-to-Broadband Coefficients

Satellites can provide global coverage of a number of climatically important radiative parameters, including broadband (BB) shortwave (SW) and longwave (LW) fluxes at the top of the atmosphere (TOA) and surface. These parameters can be estimated from narrowband (NB) Geostationary Operational Environmental Satellite (GOES) data, but their accuracy is highly dependent on the validity of the narrowband-to-broadband (NB-BB) conversion formulas that are used to convert the NB fluxes to broadband values. The formula coefficients have historically been derived by regressing matched polarorbiting satellite BB fluxes or radiances with their NB counterparts from GOES (e.g., Minnis et al., 1984). More recently, the coefficients have been based on matched Earth Radiation Budget Experiment (ERBE) and GOES-6 data (Minnis and Smith, 1998). The Clouds and the Earth's Radiant Energy Budget (CERES see Wielicki et al. 1998)) project has recently developed much improved Angular Distribution Models (ADM; Loeb et al., 2003) and has higher resolution data compared to ERBE. A limited set of coefficients was also derived from matched GOES-8 and CERES data taken on Topical Rainfall Measuring Mission (TRMM) satellite (Chakrapani et al., 2003; Doelling et al., 2003). The NB-BB coefficients derived from CERES and the GOES suite should yield more accurate BB fluxes than from ERBE, but are limited spatially and seasonally. With CERES data taken from Terra and Aqua, it is now possible to derive more reliable NB-BB coefficients for any given area. Better TOA fluxes should translate to improved surface radiation fluxes derived using various algorithms. As part of an ongoing effort to provide accurate BB flux estimates for the Atmospheric Radiation Measurement (ARM) Program, this paper documents the derivation of new NB-BB coefficients for the ARM Southern Great Plains (SGP) domain and for the Darwin region of the Tropical Western Pacific (DTWP) domain.

Khaiyer, Mandana M.↗

Overview of CERES Cloud Properties Derived From VIRS AND MODIS DATA

Simultaneous measurement of radiation and cloud fields on a global basis is recognized as a key component in understanding and modeling the interaction between clouds and radiation at the top of the atmosphere, at the surface, and within the atmosphere. The NASA Clouds and Earth s Radiant Energy System (CERES) Project (Wielicki et al., 1998) began addressing this issue in 1998 with its first broadband shortwave and longwave scanner on the Tropical Rainfall Measuring Mission (TRMM). This was followed by the launch of two CERES scanners each on Terra and Aqua during late 1999 and early 2002, respectively. When combined, these satellites should provide the most comprehensive global characterization of clouds and radiation to date. Unfortunately, the TRMM scanner failed during late 1998. The Terra and Aqua scanners continue to operate, however, providing measurements at a minimum of 4 local times each day. CERES was designed to scan in tandem with high resolution imagers so that the cloud conditions could be evaluated for every CERES measurement. The cloud properties are essential for converting CERES radiances shortwave albedo and longwave fluxes needed to define the radiation budget (ERB). They are also needed to unravel the impact of clouds on the ERB. The 5-channel, 2-km Visible Infrared Scanner (VIRS) on the TRMM and the 36-channel 1-km Moderate Resolution Imaging Spectroradiometer (MODIS) on Terra and Aqua are analyzed to define the cloud properties for each CERES footprint. To minimize inter-satellite differences and aid the development of useful climate-scale measurements, it was necessary to ensure that each satellite imager is calibrated in a fashion consistent with its counterpart on the other CERES satellites (Minnis et al., 2006) and that the algorithms are as similar as possible for all of the imagers. Thus, a set of cloud detection and retrieval algorithms were developed that could be applied to all three imagers utilizing as few channels as possible while producing stable and accurate cloud properties. This paper discusses the algorithms and results of applying those techniques to more than 5 years of Terra MODIS, 3 years of Aqua MODIS, and 4 years of TRMM VIRS data.

Minis, Patrick↗

Chapter 2: Optical Properties of the Water Column

In this chapter, and in chapter 29, the basic inter-relationship between the flux of radiant energy through the water column and the fixation of carbon by the phytoplankton in the ocean through processes of photosynthesis or primary production will be discussed.

photosynthesis↗

Improved Thin Cirrus and Terminator Cloud Detection in CERES Cloud Mask

Thin cirrus clouds account for about 20-30% of the total cloud coverage and affect the global radiation budget by increasing the Earth's albedo and reducing infrared emissions. Thin cirrus, however, are often underestimated by traditional satellite cloud detection algorithms. This difficulty is caused by the lack of spectral contrast between optically thin cirrus and the surface in techniques that use visible (0.65 micron ) and infrared (11 micron ) channels. In the Clouds and the Earth s Radiant Energy System (CERES) Aqua Edition 1 (AEd1) and Terra Edition 3 (TEd3) Cloud Masks, thin cirrus detection is significantly improved over both land and ocean using a technique that combines MODIS high-resolution measurements from the 1.38 and 11 micron channels and brightness temperature differences (BTDs) of 11-12, 8.5-11, and 3.7-11 micron channels. To account for humidity and view angle dependencies, empirical relationships were derived with observations from the 1.38 micron reflectance and the 11-12 and 8.5-11 micron BTDs using 70 granules of MODIS data in 2002 and 2003. Another challenge in global cloud detection algorithms occurs near the day/night terminator where information from the visible 0.65 micron channel and the estimated solar component of 3.7 micron channel becomes less reliable. As a result, clouds are often underestimated or misidentified near the terminator over land and ocean. Comparisons between the CLAVR-x (Clouds from Advanced Very High Resolution Radiometer [AVHRR]) cloud coverage and Geoscience Laser Altimeter System (GLAS) measurements north of 60 N indicate significant amounts of missing clouds from CLAVR-x because this part of the world was near the day/night terminator viewed by AVHRR. Comparisons between MODIS cloud products (MOD06) and GLAS in the same region also show similar difficulties with MODIS cloud retrievals. The consistent detection of clouds through out the day is needed to provide reliable cloud and radiation products for CERES and other research efforts involving the modeling of clouds and their interaction with the radiation budget.

Trepte, Qing↗

The Continuous Monitoring of Desert Dust using an Infrared-based Dust Detection and Retrieval Method

Airborne dust and sand are significant aerosol sources that can impact the atmospheric and surface radiation budgets. Because airborne dust affects visibility and air quality, it is desirable to monitor the location and concentrations of this aerosol for transportation and public health. Although aerosol retrievals have been derived for many years using visible and near-infrared reflectance measurements from satellites, the detection and quantification of dust from these channels is problematic over bright surfaces, or when dust concentrations are large. In addition, aerosol retrievals from polar orbiting satellites lack the ability to monitor the progression and sources of dust storms. As a complement to current aerosol dust retrieval algorithms, multi-spectral thermal infrared (8-12 micron) data from the Moderate Resolution Imaging Spectroradiometer (MODIS) and the Meteosat-8 Spinning Enhanced Visible and Infrared Imager (SEVIRI) are used in the development of a prototype dust detection method and dust property retrieval that can monitor the progress of Saharan dust fields continuously, both night and day. The dust detection method is incorporated into the processing of CERES (Clouds and the Earth s Radiant Energy System) aerosol retrievals to produce dust property retrievals. Both MODIS (from Terra and Aqua) and SEVERI data are used to develop the method.

Duda, David P.↗

Woodburning Heaters

On Apollo missions, the Lunar Module sewed as home and operating base for astronauts exploring the lunar surface. Since the moon has no layer of atmosphere to filter the sun's rays, the Lunar Module was exposed to extremely high daylight temperatures. To help cool the spacecraft, NASA employed a protective exterior coating capable of casting off, rather than absorbing, the sun's radiant energy. NASA selected an existing high temperature coating called Pyromark and asked the manufacturer to improve it to space-use specifications. Developed by Tempil Division of Big Three Industries, South Plainfield, New Jersey, Pyromark proved effective on the Lunar Module and it is similarly used on the Space Shuttle.

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